UNS Conference Portal, The 1st International Conference on Science, Mathematics, Environment and Education 2017

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Related Wheel Graphs and Its Locating Edge Domination Number
Robiatul Robiatul Adawiyah, Dafik Dafik Dafik, slamin slamin slamin, ika hesti agustin

Last modified: 2017-07-09


A subset $S$ of $E(G)$ is called an edge dominating set of $G$ if
every edge not in $S$ is adjacent to some edge in $S$. In this paper, we initiate to study a new concept in edge dominating set.
It is locating edge dominating set. A set $D \subseteq E$ is a locating
edge dominating set if every two edges $e_1, e_2 \in E(G) \setminus
D$ satisfy that $\emptyset \neq N(e_1) \cap D \neq N(e_2) \cap D  \neq \emptyset$.
The location edge domination number $\gamma_L' (G)$ is the minimum cardinality of locating edge dominating set.
In this research, we analyze the locating edge dominating number of some related wheel graphs. We also analyze the upper bound of locating edge domination number.